Question

Determine o valor aproximado do módulo do vetor VAB, sendo A = (1, 1, 2) e B = (2, 3, -1)
a)4,12
b)3,74
c)2,53
d)1,28
e)5,62

Answer 1

Olá


Resposta correta, letra B) 3,74


A = (1, 1, 2)
B = (2, 3, -1)


AB = B - A = (2, 3, -1) - (1, 1, 2) 

AB = (2-1, 3-1, -1-2)

AB = (1, 2, -3)



Calculando o módulo


$|\vec{AB}|~=~\mathsf{ \sqrt{(1)^2+(2)^2+(-3)^2} }\\\\\\|\vec{AB}|~=~\mathsf{ \sqrt{1+4+9} }\\\\\\|\vec{AB}|~=~\mathsf{ \sqrt{14} }\\\\\\\boxed{|\vec{AB}|~\approx~\mathsf{ 3,74}}$